While Asterius will still enter his second phase at 50% max HP as well as gain brief invulnerability, he must be killed in order to progress in the Elysium stadium encounter, instead of calling off the fight at 20% max HP.

How do you kill Asterius Hades?

For players wondering how to beat Asterius, it's simply a matter of dodging his double axe swing, leaping attack, and bull rush and then attacking when there's an opening. Once at half health, Asterius will start producing shockwaves with his attacks.

Should I kill Theseus or Asterius first?

Once you make it to the boss room to face Theseus and the Minotaur, your first goal should be to defeat Asterius. Focus on the bull because both he and Theseus have a second phase once they reach half health. The minotaur becomes a little more aggressive but doesn't change too much.